Ercole, GreyPereira, Gilberto de Assis2023-02-032023-02-032020ERCOLE, G.; PEREIRA, G. de A. An optimal pointwise Morrey-Sobolev inequality. Journal of Mathematical Analysis and Applications, v. 489, n. 1, artigo 124143, 2020. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0022247X2030305X>. Acesso em: 06 jul. 2022.0022-247Xhttp://www.repositorio.ufop.br/jspui/handle/123456789/16111Let Ω be a bounded, smooth domain of RN , N ≥ 1. For each p > N we study the optimal function s = sp in the pointwise inequality |v(x)| ≤ s(x) ∇vLp(Ω) , ∀ (x, v) ∈ Ω × W1,p 0 (Ω). We show that sp ∈ C0,1−(N/p) 0 (Ω) and that sp converges pointwise to the distance function to the boundary, as p → ∞. Moreover, we prove that if Ω is convex, then sp is concave and has a unique maximum point.en-USrestritoDirac delta distributionInfinity LaplacianArtigo publicado em periodicohttps://www.sciencedirect.com/science/article/pii/S0022247X2030305Xhttps://doi.org/10.1016/j.jmaa.2020.124143